Binary friction tensor for Brownian particles : overcoming spurious finite-size effects

TL;DR

This paper develops a method to accurately compute the binary friction tensor for Brownian particles, addressing finite-size effects and improving the understanding of particle interactions in confined systems.

Contribution

It introduces a novel approach to extract the binary friction tensor from force correlation functions, overcoming limitations of previous methods in finite systems.

Findings

Method effectively captures binary friction tensor in finite systems

Application to hard spheres demonstrates accuracy

Addresses spurious effects in finite-size simulations

Abstract

Starting from a careful analysis of the coupled Langevin equations for two interacting Brownian particles, we derive a method for extracting the binary friction tensor from the correlation function matrix of the instantaneous forces exerted by the bath particles on the fixed Brownian particles, and from the relaxation of the total momentum of the bath in a {\it finite} system. The general methodology, which circumvents the pitfalls associated with the inversion of the thermodynamic and long time limits, is applied to the case of two Brownian hard spheres in a bath of light spheres.